44 research outputs found
Linear Assignment Maps for Correlated System-Environment States
An assignment map is a mathematical operator that describes initial
system-environment states for open quantum systems. We reexamine the notion of
assignments, introduced by Pechukas, and show the conditions assignments can
account for correlations between the system and the environment, concluding
that assignment maps can be made linear at the expense of positivity or
consistency is more reasonable. We study the role of other conditions, such as
consistency and positivity of the map, and show the effects of relaxing these.
Finally, we establish a connection between the violation of positivity of
linear assignments and the no-broadcasting theorem.Comment: 6 pages, 1 tabl
Unification of witnessing initial system-environment correlations and witnessing non-Markovianity
We show the connection between a witness that detects dynamical maps with
initial system-environment correlations and a witness that detects
non-Markovian open quantum systems. Our analysis is based on studying the role
that state preparation plays in witnessing violations of contractivity of open
quantum system dynamics. Contractivity is a property of some quantum processes
where the trace distance of density matrices decrease with time. From this, we
show how a witness of initial-correlations is an upper bound to a witness of
non-Markovianity. We discuss how this relationship shows further connections
between initial system-environment correlations and non-Markovianity at an
instance of time in open quantum systems.Comment: 5 page
Vanishing quantum discord is not necessary for completely-positive maps
The description of the dynamics of a system that may be correlated with its
environment is only meaningful within the context of a specific framework.
Different frameworks rely upon different assumptions about the initial
system-environment state. We reexamine the connections between
complete-positivity and quantum discord within two different sets of
assumptions about the relevant family of initial states. We present an example
of a system-environment state with non-vanishing quantum discord that leads to
a completely-positive map. This invalidates an earlier claim on the necessity
of vanishing quantum discord for completely-positive maps. In our final remarks
we discuss the physical validity of each approach.Comment: close to published versio
Operational Markov condition for quantum processes
We derive a necessary and sufficient condition for a quantum process to be
Markovian which coincides with the classical one in the relevant limit. Our
condition unifies all previously known definitions for quantum Markov processes
by accounting for all potentially detectable memory effects. We then derive a
family of measures of non-Markovianity with clear operational interpretations,
such as the size of the memory required to simulate a process, or the
experimental falsifiability of a Markovian hypothesis.Comment: 5+3 pages, 4 figures; split off from earlier version of
arXiv:1512.0058
Recommended from our members
Quantum Stochastic Walks: A Generalization of Classical Random Walks and Quantum Walks
We introduce the quantum stochastic walk (QSW), which determines the evolution of a generalized quantum-mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical, and quantum-stochastic transitions from a vertex as defined by its connectivity. We show how the family of possible QSWs encompasses both the classical random walk (CRW) and the quantum walk (QW) as special cases but also includes more general probability distributions. As an example, we study the QSW on a line and the glued tree of depth three to observe the behavior of the QW-to-CRW transition.Chemistry and Chemical Biolog
Recommended from our members
Time-Dependent Density Functional Theory for Open Quantum Systems with Unitary Propagation
We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potential. A Markovian bath functional inspired by the theory of nonlinear Schrödinger equations is suggested, which can be readily implemented in currently existing real-time codes. Finally, calculations on a helium model system are presented.Chemistry and Chemical Biolog
Lazy states: sufficient and necessary condition for zero quantum entropy rates under any coupling to the environment
We find the necessary and sufficient conditions for the entropy rate of the
system to be zero under any system-environment Hamiltonian interaction. We call
the class of system-environment states that satisfy this condition lazy states.
They are a generalization of classically correlated states defined by quantum
discord, but based on projective measurements of any rank. The concept of lazy
states permits the construction of a protocol for detecting global quantum
correlations using only local dynamical information. We show how quantum
correlations to the environment provide bounds to the entropy rate, and how to
estimate dissipation rates for general non-Markovian open quantum systems.Comment: 4 page
Positivity in the presence of initial system-environment correlation
The constraints imposed by the initial system-environment correlation can
lead to nonpositive Dynamical maps. We find the conditions for positivity and
complete positivity of such dynamical maps by using the concept of an
assignment map. Any initial system-environment correlations make the assignment
map nonpositive, while the positivity of the dynamical map depends on the
interplay between the assignment map and the system-environment coupling. We
show how this interplay can reveal or hide the nonpositivity of the assignment
map. We discuss the role of this interplay in Markovian models.Comment: close to the published version. 5 pages, 1 figur